Potential bug of function Reduce

Question

Bug introduced in 11.1 or earlier and fixed in 11.3.0

Just a simple expression in version 11.2, Windows 10

Reduce[(-2)^n > 1, n, Integers]

returns

n ∈ Integers && n >= 2

But this result is not correct because it should be

n / 2 ∈ Integers && n >= 2

Furthermore, I remember that in previous version, e.g. 10.x, Reduce works properly.

Update

Wolfram Alpha behaves inconsistently.

I'm voting to close this question as off-topic because there is no question in the post. This is just a bug report to which an answer cannot be supplied. — QuantumDot, Dec 12 '17 at 17:02
This kind of bug I observed also when Reduce dealt with equations, see edit to this answer Solving a diophantine equation with three variables — Artes, Dec 13 '17 at 14:48
@Kuba Yes, reported. But WRI seemed to show little interest, as I see it. — Αλέξανδρος Ζεγγ, Dec 14 '17 at 08:47
@AlexanderZeng because they did not reply or because of what they said? — Kuba, Dec 14 '17 at 11:22
@AlexanderZeng can you post this bug on community.wolfram.com. I am pretty sure a representative will see it ! — Ali Hashmi, Dec 14 '17 at 23:58
@Kuba Because I think the reporter was treated as a help seeker, but s/he should be a help deliverer. — Αλέξανδρος Ζεγγ, Dec 15 '17 at 05:36
@AliHashmi So, if necessary, maybe you can report it instead. — Αλέξανδρος Ζεγγ, Dec 16 '17 at 11:48

score 5 · Accepted Answer · answered Dec 14 '17 at 13:37

Strangely, adding a pointless equation causes the bug to be avoided:

aux = Reduce[(-2)^n > 1 && n == m, n, Integers]
(*  (m | n | C[1]/2) ∈ Integers && C[1] >= 2 && m == C[1] && n == C[1]  *)

I found it tricky to eliminate the unwanted variables programmatically. Eliminate does not work on inequalities, nor will Reduce or Solve eliminate a variable from aux probably for the same reason.

Or @@ (aux /. Solve[
     Cases[aux, eq_Equal],
     DeleteCases[n]@ Variables@ Cases[aux, Equal[x_, y_] :> {x, y}]
     ]) // Reduce
(*  n/2 ∈ Integers && n >= 2  *)

Potential bug of function Reduce

1 Answers1